Juanita’s Social Security full monthly retirement benefit is $2,128. She started collecting Social Security at age 65. Her benefit is reduced since she started collecting before age 67. Using the reduction percents from Example 1, find her approximate monthly Social Security benefit to the nearest dollar.EXAMPLE 1Marissa from Example 2. What will her monthly benefit be, since she did not wait until age 67 to receive full retirement benefits?SOLUTION Age 67 is considered to be full retirement age if you were born in 1945. If you start collecting Social Security before age 67, your full retirement benefit is reduced, according to the following schedule.• If you start at collecting benefits at 62, the reduction is about 30%.• If you start at collecting benefits at 63, the reduction is about 25%.• If you start at collecting benefits at 64, the reduction is about 20%.• If you start at collecting benefits at 65, the reduction is about 13.3%.• If you start at collecting benefits at 66, the reduction is about 6.7%.Marissa’s full retirement benefit was $1,130.40. Since she retired at age 65, the benefit will be reduced about 13.3%.Find 13.3% of $1,130.40, and round to the nearest cent.0.133 x 1,130.40Subtract to find the benefit Marissa would receive.1,130.40 x 150.34Marissa’s benefit would be about $980.06.EXAMPLE 2Marissa reached age 62 in 2007. She did not retire until years later. Over her life, she earned an average of $2,300 per month after her earnings were adjusted for inflation. What is her Social Security full retirement benefit?

Answer:

b

Step-by-step explanation:

The sum of angles in a triangle is 180°. Therefore,

x - 11 + 48 + 90 = 180

x + 127 = 180

x = 53°

Answer:

x = 53

Step-by-step explanation:

Using the information that angles in a triangle add up to 180°, we can set up and equation to find the value of x

⇒ Use the information that angles in a triangle add up to 180°, form an equation

→ x - 11 + 48 + 90 = 180

⇒ Simplify

→ x + 127 = 180

⇒ Minus 127 from both sides to isolate x

→ x = 53

We can substitute the value of x back into x - 11 + 48 + 90 = 180 to see if our value of x is correct, if we end up on 180 on both sides then the value of x is correct

→ x - 11 + 48 + 90 = 180

⇒ Substitute in the value of x

→ 53 - 11 + 48 + 90 = 180

⇒ Simplify

→ 180 = 180

This means that x = 53 is correct

Using the given information that sin A = -5/6 and A is in Quadrant 3, the correct value for sin(2A) is -5√11/36

Given sin A = -5/6 and A in Quadrant 3, we can use the double-angle formula for sine to find sin(2A). The formula states that sin(2A) = 2sin(A)cos(A).

First, we need to find the value of cos(A). Since sin A = -5/6, we can use the Pythagorean identity sin^2(A) + cos^2(A) = 1 to solve for cos(A). In Quadrant 3, sin(A) is negative and cos(A) is negative or zero. Solving the equation:

sin^2(A) + cos^2(A) = 1

(-5/6)^2 + cos^2(A) = 1

25/36 + cos^2(A) = 1

cos^2(A) = 1 - 25/36

cos^2(A) = 11/36

Taking the square root of both sides, we find cos(A) = -√11/6. Since A is in Quadrant 3, cos(A) is negative.

Now, we can substitute the values into the double-angle formula:

sin(2A) = 2sin(A)cos(A)

sin(2A) = 2(-5/6)(-√11/6)

sin(2A) = -5√11/36

Therefore, the correct answer for sin(2A) is -5√11/36.

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Answer:

1/2

Step-by-step explanation:

To multiply fractions, you multiply numerator with numerator and denominator with denominator:

a/b*c/d=(a*c)/(b*d)

5/6*18/30=(5*18)/(6*30)=90/180=9/18=1/2

Therefore, the answer is 1/2. Looks like your answer of 113/30 either is wrong or the problem was not formatted correctly.

Answer:

BC ≈ 14.5 cm

Step-by-step explanation:

Using the sine ratio in the right triangle

sin65° = \(\frac{opposite}{hypotenuse}\) = \(\frac{BC}{AB}\) = \(\frac{BC}{16}\) ( multiply both sides by 16 )

16 × sin65° = BC , then

BC ≈ 14.5 cm ( to the nearest tenth )

a. The function is not strictly convex.Now, let's check the homotheticity of the function. A function is homothetic if it is continuous, quasiconcave and there exists a positive function, v(x1), such that u(x)=v(x1)f(x2).  b. We can say that the function is homothetic.

We are also given the values of L, X and the utility function. The values are\(L=2,X=(−[infinity],[infinity])×R +​,\)≿ is represented by the utility function\(u(x)=x 1​+ln(1+x 2​).\)

Let's solve this.

Suppose the utility function u(x) is represented as:

\(u(x)=x 1​+ln(1+x 2​)\)

We can see that the utility function is quasilinear. It has a linear component in x1 and a quasi-linear component in x2.

Therefore, we can say that the utility function is quasilinear.Now, let's check the convexity of the utility function. We will find the Hessian matrix and check its properties. The Hessian matrix is given by: H = [0 0; 0 1/(1+x2)^2]The determinant of \(H is 0(1/(1+x2)^2)-0(0) = 0\), which is neither positive nor negative.

Hence, the Hessian matrix is neither positive definite nor negative definite.

Therefore, we cannot determine whether the function is convex or concave.

However, we can check the strict convexity of the function by checking if the Hessian matrix is positive definite or not. The eigenvalues of the Hessian matrix are 0 and \(1/(1+x2)^2\), which are non-negative.

Hence, the Hessian matrix is positive semi-definite.

Therefore, the function is not strictly convex.Now, let's check the homotheticity of the function. A function is homothetic if it is continuous, quasiconcave and there exists a positive function, v(x1), such that \(u(x)=v(x1)f(x2)\)

If we take \(v(x1) = x1, then u(x)=x1(1+ln(1+x2)) = x1ln(e^(1+x2)) = ln(e^(1+x2)^x1)\)

Therefore, we can say that the function is homothetic.

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Answer:

the answe is X= 14/ A :)

explanation: I took the exam review good luck!

Answer:

It is A

Step-by-step explanation:

edge 2022

The length of XZ is 5.5 m.

The length of side XZ is calculated by applying the following cosine and sine rule.

If the length of WY is 7 m, then ∠WYZ is calculated as follows;

cos Y = (z² + w² - y² ) / (2zw)

where;

cos Y = ( 7² + 5.1² - 3² ) / ( 2 x 7 x 5.1 )

cos Y = 0.9245

Y = cos⁻¹ (0.9245)

Y = 22.4⁰

The value of ∠WYX is calculated as follows;

cos Y = (x² + w² - y² ) / (2xw)

cos Y = ( 7² + 5² - 4.8² ) / ( 2 x 7 x 5)

cos Y = 0.728

Y = cos⁻¹ (0.728)

Y = 43.28⁰

The value of ∠ZYX = 43.28⁰ + 22.4⁰ = 65.68⁰

The length of XZ is calculated by using the following cosine rule.

|XZ|² = |XY|² + |ZY|² - (2 x |XY| x |XY|) cos Y

|XZ|² = 5² + 5.1²  -  (2 x 5 x 5.1 ) x cos (65.68)

|XZ|² = 30

|XZ| = √30

|XZ| = 5.5 m

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(a) The number of choices with no restriction is 10,000.

(b) The number of choices with no repeated digits is 5,040.

(c) The number of choices with no repeated digits and the third digit as 0 is 648.

(a) With no restriction, there are 10 choices for each digit, ranging from 0 to 9. Since a 4-digit pin code consists of four digits, the total number of choices is 10^4 = 10,000.

(b) When no digit is repeated, the number of choices for the first digit is 10. For the second digit, there are 9 choices remaining (as one digit has been used). Similarly, for the third digit, there are 8 choices remaining, and for the fourth digit, there are 7 choices remaining. Therefore, the total number of choices is 10 × 9 × 8 × 7 = 5,040.

(c) When no digit is repeated and the third digit is fixed as 0, the number of choices for the first digit is 9 (excluding 0). For the second digit, there are 9 choices remaining (as one digit has been used, but 0 is available).

For the fourth digit, there are 8 choices remaining (excluding 0 and the digit used in the second position). Therefore, the total number of choices is 9 × 9 × 8 = 648.

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The sandwich and soup combos that can be served is 48.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 1/3 liter of soup is served with each sandwich and soup combo.

Since the cook made 16 liters of soup to serve with sandwiches as part of the combo. The sandwich and soup combination will be:

= 16 ÷ 1/3.

= 16 × 3

= 48

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Answer:

40 ft

Step-by-step explanation:

The approximate air pressure at the center of a hurricane is 910 millibars.

Given,

The mean sustained wind velocity equation, v = 6.3 × √(1013 - p)

p is the air pressure in millibars

The mean sustained wind velocity - 64 meters per second.

We have to find the approximate air pressure.

Here,

The equation for wind velocity ;

v = 6.3 × √(1013 - p)

v is given 64

Then substitute;

64 = 6.3 × √1013 - p

64/6.3 = √1013 - p

10.16 = √1013 - p

Square both sides

(10.16)² = (√1013 - p)²

We get,

103.23 = 1013 - p

p = 1013 - 103.33 = 909.67 ≈ 910 millibars

That is,

The approximate air pressure at the center of a hurricane is 910 millibars.

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Answer:

\(\sqrt{2000}\phantom{a}yards\)

Step-by-step explanation:

For a right triangle, \(a^{2} =b^{2} +c^{2}\), if a is the hypotenuse. So, \(60^{2} =40^{2} +c^{2}\), and c is the the distance we are trying to find:

\(60^{2} =40^{2} +c^{2}\)

\(3600=1600+c^{2}\)

\(c^{2} =2000\)

\(c=\sqrt{2000}\phantom{a} yards\)

The equilibrium point for the supply and demand equations p² + 4q = 253 and 183p² + 6q = 0 is (q, p) = (3, 10).

To find the equilibrium point, we need to solve the system of equations formed by the supply and demand equations. By substituting the value of q = 3 into the first equation, we get p² + 4(3) = 253, which simplifies to p² + 12 = 253.

Solving this equation gives us p = 10. Substituting the values of q = 3 and p = 10 into the second equation, we get 183(10)² + 6(3) = 0, which simplifies to 18300 + 18 = 0.

Since this equation holds true, we have found the equilibrium point to be (q, p) = (3, 10), where the equilibrium quantity is q = 3 and the equilibrium price is p = 10.

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Answer:

Read below.

Step-by-step explanation:

There is an infinite amount of numbers larger than 0.68 but here are some for you:

1, 2, 3.4, 4.1289, 190, 2198, 0.7, 0.72578

Answer:

- x = 81 and 3/4

Step-by-step explanation:

8 × 2 – 4x = 363

16 - 4x = 363

Subtract 16 from each side:

16 - 16 - 4x = 363 - 16

- 4x = 327

Divide each side by 4:

- 4x  ÷ 4 = 327 ÷ 4

- x = 81 and 3/4

To determine the depth that should be added to the warehouse to minimize annual inventory costs, we need to consider the economic order quantity (EOQ) formula.

The EOQ formula helps us find the optimal order quantity that minimizes the total annual inventory costs, taking into account both ordering costs and carrying costs.

First, let's calculate the EOQ using the given information:

Demand (D) = 12,000 lawn mowers per year

Ordering cost (S) = $30 per order

Carrying cost per unit (H) = $2 per lawn mower per year

EOQ = sqrt((2 * D * S) / H)

Substituting the values:

EOQ = sqrt((2 * 12,000 * 30) / 2) = sqrt(360,000) = 600

The economic order quantity is 600 lawn mowers. This means that the optimal order quantity to minimize costs is 600 lawn mowers per order.

Now, let's calculate the total area required to store the lawn mowers. Each lawn mower box has dimensions of 5 feet by 4 feet by 2 feet, which gives us a volume of 5 * 4 * 2 = 40 cubic feet per lawn mower.

The total volume of lawn mowers can be calculated as:

Volume of lawn mowers = EOQ * 40 cubic feet

Since we can only use 60% of the warehouse for storing the lawn mowers, the area required for the lawn mowers can be calculated as:

Area required = (EOQ * 40 cubic feet) / 0.6

Given that the warehouse is currently 25 feet wide by 40 feet deep, we need to find the additional depth (D) required. Let's solve for D:

25 * (40 + D) = Area required

Substituting the values:

25 * (40 + D) = (EOQ * 40 cubic feet) / 0.6

25 * (40 + D) = (600 * 40 cubic feet) / 0.6

25 * (40 + D) = 40,000 cubic feet

Dividing both sides by 25:

40 + D = 1,600

Subtracting 40 from both sides:

D = 1,600 - 40 = 1,560

Therefore, the warehouse should be increased by 1,560 feet in depth (or length) to minimize the annual inventory costs.

As for how much the company should be willing to pay for this addition, it would depend on the cost of extending the warehouse. The company should consider factors such as construction costs, permits, materials, labor, and any other associated expenses. The decision should be based on a cost-benefit analysis, comparing the estimated cost of the addition with the potential savings in inventory costs over time.

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If only two out of the five people show up for the meeting, it is possible in 10 different ways.

If five people plan to meet after school and there will be one group of five people if they all show up, but only two people show up, we need to determine the number of ways this can happen.

To find the number of ways two people can show up out of the five, we can use combinations. In a combination, the order of selection does not matter.

The number of ways to choose two people out of five can be calculated using the formula for combinations, denoted as "nCr", where n is the total number of people and r is the number of people we want to choose.

In this case, we want to choose 2 people out of 5, so the calculation would be:

5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 \(\times\) 4)/(2 \(\times\) 1) = 10

Therefore, there are 10 possible ways for two people to show up out of the five if all of them plan to meet after school.

These 10 possibilities could be different combinations of any two individuals out of the five.

To determine the specific combinations, you can list all the pairs or use a combination formula calculator.

It's important to note that the order in which the two people show up does not matter, as long as they are two out of the five originally planning to meet.

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Answer:

False

Step-by-step explanation:

The function isn't continuous at x=±2 as a function isn't continuous at the point where the function becomes undefined, this function becomes undefined when the denominator is equal to 0. So x^2-4=0 => x=±2.

Answer:    Since the angles in a triangle sum up to 180 degrees, we can write:

m∠O + m∠P + m∠Q = 180

Substituting the given angle measures, we get:

(2x - 5) + (3x - 8) + (10x - 17) = 180

Simplifying and solving for x, we have:

15x - 30 = 180

15x = 210

x = 14

Now that we know x = 14, we can find the value of angle θ by substituting x into one of the angle measures:

m∠O = 2x - 5 = 2(14) - 5 = 23 degrees

Therefore, the value of angle θ is 23 degrees and the value of x is 14.

Step-by-step explanation: hope this helps (:

Answer:

G(x) = 2x - 3 has a linear inverse which is a function.

k(x) = -9x2 has a square root inverse that is a function on only the interval x < 0.

Step-by-step explanation:

The inverse of a function is a reflection across the y=x line. This results in switching the values of the input and output or (x,y) points to become (y,x). This can be done algebraically in an equation as well. Begin by switching the x and y in the equation then solve for y.

x = 2y - 3 -------> y = x/2 + 3/2 is linear and a function.

-9y2 = x --------> y = √(-x/9)  is a square root that is a function on only the interval x < 0.

Absolute value does not have an inverse function.

x = -20 is a vertical line which is not a function.

Brainliest please?

Answer:

Step-by-step explanation:

try D

Answer:

C. is the correct answer.

Step-by-step explanation:

l = -0.275t + 81

or, 70 = -0.275×40+81

or, 70 = -11+81

so, 70 = 70 (which is true)

Answer:

Dimensions are 20 + 20 + 40 + 40

Step-by-step explanation:

A bin of 50 parts contains 5 that are defective and a sample of 10 parts is selected without replacement, then total 40,753,713 samples contain at least 4 defective parts.

A bin of 50 parts contains 5 that are defective.

A sample of 10 parts is selected without replacement.

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = Samples with precisely 4 defectives + samples with precisely 5 defects

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(^{5}C_{4}\cdot ^{45}C_{6}+ ^{5}C_{5}\cdot^{45}C_{5}\)

Using the formula \(^nC_{r} = \frac{n!}{r!(n-r)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!(5-4)!}\cdot\frac{45!}{6!(45-6)!}+\frac{5!}{5!(5-5)!}\cdot\frac{45!}{5!(45-5)!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5!}{4!1!}\cdot\frac{45!}{6!39!}+\frac{5!}{5!0!}\cdot\frac{45!}{5!40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = \(\frac{5\times4!}{4!\times1}\cdot\frac{45\times44\times43\times42\times41\times40\times39!}{6\times5\times4\times3\times2\times1\times39!}+1\cdot\frac{45\times44\times43\times42\times41\times40!}{5\times4\times3\times2\times1\times40!}\)

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 5 × 15 × 44 × 43 × 7 × 41 + 1 × 9 × 11 × 7 × 41

Number of samples of size 10 from 50 pieces, at least 4 of which are faulty = 40,753,713

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Answer:

21

6 CM REMAINED

Step-by-step explanation:

Convert metre to centimetre

100 cm = 1 m

3 m = 3 x 100 = 300cm

strips cut = 300/14 = 21 would be cut with some remainders

Remainders = 300 - (14 x 21) = 6cm